D1 - Gravitational Fields

Question 1

what is gravity

Answer 1

all mass attracts all other mass

Question 2

what is the gravitational force eq

Answer 2

F = GMm/r^2

Question 3

what are the relationships present in the gravitational force eq

Answer 3

F is directly proportional to Mm and inversely proportional to r^2

Question 4

what are the si units for the grav constant

Answer 4

kg-1m3s-2

Question 5

what is newtons shell theorem

Answer 5

a spherically symmetric shell of mass M acts as if all of its mass is located at the centre

Question 6

determine the force of gravitational attraction between the earth (m- 5.98 x 10^24kg) and a 70kg student if the student is in an airplane at 40000ft above the earths surface. this would place them 6.39 x 10^6m from the earths centre

Answer 6

F = GMm/r^2
F = (6.67x10^-11) x (5.98 x 10^24)(70)/(6.39 x 10^6)^2
F = 683.79N

Question 7

what is a vector field

Answer 7

a field that describes the force that would act on a particle at various positions

Question 8

what is the formula for an electric field

Answer 8

E = force/charge

Question 9

how does mass relate to the distortion of space

Answer 9

the larger the mass, the more space that it distorted

Question 10

how do we represent the strength of a field

Answer 10

vector length
vector density

Question 11

what is a newton in si units

Answer 11

kgms-2

Question 12

what does ‘r’ mean in the gravitational force eq in relation to the earth

Answer 12

r = radius of the whole orbit to the centre of earth

Question 13

what is the formula for gravitational field strength

Answer 13

g=GM/r^2

Question 14

what is the gravitational field strength halfway between the centres of the earth and the moon?
M of earth = 6 x 10^24kg
m of moon = 7.3 x 10^22kg
radius between earth and moon = 3.8 x 10^8m

Answer 14

g = GM/r^2
g = (6.67 x 10^-11)(6x10^24)/(1.9x10^8)^2
g = 0.011 of earth

g = (6.67x10^-11)(7.3 x 10^22)/(1.9x10^8)^2
g = 1.35x10^-4

0.011-1.35x10^-4 = 0.0109Nkg^-1 to the earth

Question 15

what happens to the work done the further you go from a planet

Answer 15

GPE increases with distance, but if an object is far enough away from the planet, the grav force is negligible

Question 16

what is teh formula for grav potential (V)

Answer 16

V = W/m
Grav potential = work done/ mass

Question 17

what is the grav potential energy at infinity

Answer 17

zero

Question 18

what is gravitational potential

Answer 18

the gravitational potential energy per unit of mass

Question 19

when drawing equipotentials around the earth to represent grav potential, what do you notice about the spaces between the lines?

Answer 19

the equipotentials get more spaced out

Question 20

Does the grav potential start from negative or positive? why

Answer 20

negative.

as the distance from the earth increases, the grav potential gets closer to zero, and so the closer distances have to have a negative grav potential for this to happen

Question 21

as the distance from the earth increases, the grav potential…

Answer 21

decreases, because the point is further away from the grav. field

Question 22

what does the potential gradient equal

Answer 22

gravitational field strength

Question 23

what is the work done by a mass when it is moved along an equipotential surface

Answer 23

no work is done, when a mass is moved ALONG an equipotential line

Question 24

calculate the minimum work required to lift an astronaut of mass 80kg from the earth’s surface to the height of the ISS (300km).

earth radius = 6400km
earth mass = 6x10^24
g = 6.67 x 10^-11

Answer 24

Work done = mass x change in grav potential
change in grav potential = grav potential at earth - grav potential at ISS
grav potential at earth = 6.26x10^7
grav potential at ISS = -5.97 x 10^7
6.26x10^7 - 5.97 x 10^7 = 2.9 x 10^6
(2.9 x10^6)(80) = 232000000J or 232MJ

Question 25

what is the formula for potential gradient

Answer 25

change in grav potential/change in radius